Abstract
Solving the forward kinematics of parallel robots efficiently is important for real-time applications. However, it remains a difficult problem due to its high nonlinearity. This paper combines artificial neural networks and the Global Newton-Raphson with Monotonic Descent (GNRMD) algorithm to decrease the training sets of neural networks while avoiding divergence problem. Furthermore, simplified Newton iteration is introduced to reduce the duration of solution time. The proposed method is demonstrated taking a Stewart platform as an example and the nonlinear equations are established with the geometrical method. Based on the continuous characteristic of real-time applications, the result of the previous solution cycle is used as the initial value of the current solution cycle. Moreover, a threshold adjusting the effective scope of GNRMD algorithm and simplified Newton iteration is set to balance the efficiency and number of iteration. The performance of the algorithm is verified in the environment of Microsoft Visual Studio 2013 based on the continuous feedback of the Stewart platform. Besides, it is compared with GNRMD algorithm and a higher-order numerical method. The results indicate that the proposed algorithm can improve the efficiency of solving the forward kinematics problem.
Highlights
Parallel robots have been extensively studied for decades and have been widely applied to various fields due to the following advantages: high rigidity, accuracy, and load-bearing capacity [1]–[5]
Compared with the inverse kinematics problem (IKP), the forward kinematics problem (FKP) is more difficult due to the high nonlinearity and the various structures of parallel robots [6] and the efficiency for solving the FKP is important for real-time applications
We propose a method that combines artificial neural networks (ANNs) and Global Newton–Raphson with Monotonic Descent (GNRMD) algorithm to solve the FKP of parallel robots efficiently
Summary
Parallel robots have been extensively studied for decades and have been widely applied to various fields due to the following advantages: high rigidity, accuracy, and load-bearing capacity [1]–[5]. Compared with the IKP, the forward kinematics problem (FKP) is more difficult due to the high nonlinearity and the various structures of parallel robots [6] and the efficiency for solving the FKP is important for real-time applications. Zhang: Efficient Numerical Method for Forward Kinematics of Parallel Robots convergence speed It has the divergence problem if the initial value is far from the solution. We propose a method that combines ANNs and GNRMD algorithm to solve the FKP of parallel robots efficiently. ANNs can be trained with fewer sample sets because GNRMD algorithm can avoid the divergence problem even when the initial value is far from the solution.
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